As Telewest is part of Virgin, I would suspect that it is the only supplier of broadband available on that cable link.
She will have a new email address.
However if she keeps her Tiscali PAYGO account, and actually dials up about every six weeks, it will keep her dial up account open, and hence her old email address will be accessible even via broadband.
She can gradually introduce her contacts to her new email address.
I am on BT BB and use orange, and Supanet email addresses for various reasons, and as long as I dial up within 90 days for a few minutes, the accounts stay open.